This invention relates to a cutting machine having a table for the material to be cut and at least one cutting blade rotatably accommodated in a protecting casing or guard casing, a motor for driving said cutting blade in such a direction that the portion of said cutting blade projecting from the guard casing enters into said guard casing at the cutting place, a rim defining an opening of said guard casing through which said blade projects. With a prior machine of this type disclosed in U.S. Pat. No. 3,339,597 it is not possible to cut plates of plastic material, particularly of reinforced plastic material and non-ferrous metal sheets cleanly simply and accurately. Due to the cutting forces the edges of the cut are deformed locally broken away or splitted by the blade which leaves the material to be cut at the cutting place.